37042 ÷ 6 = 6173 R4
Alright, let's work through the division of 37042 by 6 step by step.

Step 1:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 2:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 36 from 37 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 3:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 61
Subtract 6 from 10 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 6

Step 4:
6 goes into 44 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 617
Subtract 42 from 44 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 5:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 6173
Subtract 18 from 22 to get 4.

The final result is 6173 with a remainder of 4.